PRIFYSGOL BANGOR BANGOR UNIVERSITY ARHOLIADAU DIWEDD SEMESTER 1 JANUARY 2014 END OF SEMESTER 1 EXAMINATIONS JANUARY 2014 YBB GRADD MEISTER BBS MASTER’S DEGREES AMSER A GANIATEIR: 2 AWR TIME ALLOWED: 2 HOURS ASB4601- Research Methods NI CHANIATEIR CYFRIFIANELLAU Y GELLIR EU RHAGLENNU NO PROGRAMMABLE CALCULATORS ARE PERMITTED. ALL QUESTIONS CARRY EQUAL MARKS All questions carry equal marks Answer ALL FIVE Questions ANSWER ALL FIVE QUESTIONS Question 1 I. Given the dataset: 20,10,40,20,10,50,60,20,30,40,50,90,20,30,50 calculate the min, max, mode, median and mean.(20%) II. Draw a boxplot with inner and outer fence (20%) III. For the data in part (i), if the value 60 was replaced by 1000, what would you call this value in the dataset? What could be the explanation for such an extreme value?(20%) IV. What would be the new values for the three measures of central location calculated in (i). Comment on the differences (20%) V. Calculate the standard deviation for this specific sample as well as infer the standard deviation for the population from which the data are drawn. Discuss the difference in the two results.(20%) Question 2 A Portfolio consists of five investment products. The expected return of each investment, in million GPB, is normally distributed as follows: Investment I ~ N(80, 16); Investment II ~ N(90, 25); Investment III ~ N(60, 9); Investment IV ~ N(50, 4); Investment V ~ N(10, 1); The returns from the five investments are independent. I. Find the distribution of the total Portfolio return. Report the mean, the variance and the standard deviation. (30%) II. If the total return exceeds 300 million GPB, a bonus will be given. What is the probability that this bonus won’t be given? (35%) III. If the total return is less than 290 million GPB, the client will look for other firms to handle his money in the future. What is the probability that the firm will keep this customer? (35%) Question 3 The following data are the Years_of_Experience of the brokers in an investment firm, and the Annual_Return_Rates they achieve for whatever funds they control. Experience (in years) 5 10 15 15 20 25 30 30 20 20 Annual_Return_Rates (%) 1 1 3 4 5 6 8 9 5 6 I. Plot the Annual_Return_Rates against Years_of_Experience and fit a straight regression model to the data. (20%) II. Plot the residuals from the model against Years_of_Experience. What does this say about the fitted model? (20%) III. What percentage of variation in Annual_Return_Rates is explained by the regression relationship? (20%) IV. if we are about to hire a new trader with 35 years of experience, what would be the expected Annual_Return_Rates for him/her? (20%) V. How is it possible to have three traders with the same years of experience (20) and different performance? Question 4 The following Stata output refers to a regression for the determinants of the return on assets for a sample of 100 banks in a particular year. The variable definitions are as follows.

1. PRIFYSGOL BANGOR
BANGOR UNIVERSITY
ARHOLIADAU DIWEDD SEMESTER 1
JANUARY 2014
END OF SEMESTER 1 EXAMINATIONS
JANUARY
2014
YBB GRADD MEISTER
BBS MASTER’S DEGREES
AMSER A GANIATEIR:
2 AWR
TIME ALLOWED:
2 HOURS
ASB4601- Research Methods
NI CHANIATEIR CYFRIFIANELLAU Y GELLIR EU
RHAGLENNU
NO PROGRAMMABLE CALCULATORS ARE PERMITTED.
ALL QUESTIONS CARRY EQUAL MARKS
All questions carry equal marks
Answer ALL FIVE Questions

2. ANSWER ALL FIVE QUESTIONS
Question 1
I. Given the dataset:
20,10,40,20,10,50,60,20,30,40,50,90,20,30,50 calculate the min,
max, mode, median and mean.(20%)
II. Draw a boxplot with inner and outer fence (20%)
III. For the data in part (i), if the value 60 was replaced by
1000, what would you call this value in the dataset? What could
be the explanation for such an extreme value?(20%)
IV. What would be the new values for the three measures of
central location calculated in (i). Comment on the differences
(20%)
V. Calculate the standard deviation for this specific sample as
well as infer the standard deviation for the population from
which the data are drawn. Discuss the difference in the two
results.(20%)
Question 2
A Portfolio consists of five investment products. The expected
return of each investment, in million GPB, is normally
distributed as follows: Investment I ~ N(80, 16); Investment II
~ N(90, 25); Investment III ~ N(60, 9); Investment IV ~ N(50,
4); Investment V ~ N(10, 1); The returns from the five
investments are independent.
I. Find the distribution of the total Portfolio return. Report the
mean, the variance and the standard deviation. (30%)
II. If the total return exceeds 300 million GPB, a bonus will be
given. What is the probability that this bonus won’t be given?
(35%)
III. If the total return is less than 290 million GPB, the client
will look for other firms to handle his money in the future.
What is the probability that the firm will keep this customer?
(35%)
Question 3

3. The following data are the Years_of_Experience of the brokers
in an investment firm, and the Annual_Return_Rates they
achieve for whatever funds they control.
Experience (in years)
5
10
15
15
20
25
30
30
20
20
Annual_Return_Rates (%)
1
1
3
4
5
6
8
9
5
6
I. Plot the Annual_Return_Rates against Years_of_Experience
and fit a straight regression model to the data. (20%)
II. Plot the residuals from the model against
Years_of_Experience. What does this say about the fitted
model? (20%)
III. What percentage of variation in Annual_Return_Rates is
explained by the regression relationship? (20%)
IV. if we are about to hire a new trader with 35 years of
experience, what would be the expected Annual_Return_Rates
for him/her? (20%)
V. How is it possible to have three traders with the same years

4. of experience (20) and different performance?
Question 4
The following Stata output refers to a regression for the
determinants of the return on
assets for a sample of 100 banks in a particular year. The
variable definitions are as follows:
roa = percentage return on assets
lasset = natural logarithm of asset value (in £ billions)
list = 1 if the bank is stock market-listed, 0 otherwise.
I.
(60%) Interpret and explain the importance and the information
we get from the following results from the Stata output:
i) Coefficients on lasset and list. (10%)
ii) t-statistics and p-values of the coefficients on lasset and list.
(10%)
iii) R-squared and the Adj R-squared (10%)
iv) Root MSE (= standard error of the regression). (10%)
v) The F-statistic (10%)
vi) What is the meaning of the constant _cons in this model?
(10%)
II.
What is the expected return on assets for a non-listed bank with
an asset value of £20 billion? (40%)
Question 5
A financial firm based in US allocates the number of Analysts
according to the sum (in million $) meant to be invested in two
different sectors: real estate and foreign exchange.
The following MS Excel output refers to three regression
models for the determinants of the number of Analysts:

5. Model#1
Model#2
Model#3
I. For the first model, draw the plot of the residuals and discuss
what you can get from this plot (20%)
II. Describe and discuss the meaning of each of the statistics
(each and every number) in the second and third model. (20%)
III. Highlight any problems that require possibly further
statistical analysis in each of the three models (20%)
IV. Which model would you select and why? (10%)
V. What is the intuition behind the construction (selection of
variables) of each of these three models? (30%)
ASB-4601/4801
RESEARCH METHODS
FORMULA SHEET
Expectation, variance, covariance and correlation:
å
=
n
x
x
i
å

6. -
-
=
1
n
)
x
x
(
s
2
i
2
x
å
-
å
-
å
-
-
=
r
2
i
2
i
i
i
xy
)
y
y
(
)

7. x
x
(
)
y
y
)(
x
x
(
ˆ
Normal distribution, and sampling distributions of sample mean
and variance:
X ~ N(µx,
2
x
s
)
2
x
2
x
2
)
x
(

8. 2
x
e
2
1
)
x
(
f
s
m
-
-
ps
=
Z =
x
x
X
s
m
-
~ N(0,1)
÷
÷
ø
ö
ç
ç

9. è
æ
s
m
n
,
N
~
X
2
x
x
)
1
n
(
~
S
)
1
n
(
2
2
x
2
x
-
c
s
-
Hypothesis tests:

10. n
x
z
x
0
s
m
-
=
n
s
x
t
x
0
m
-
=
n
s
d
t
d
0
m
-
=
y
2
y

11. x
2
x
0
n
s
n
s
)
y
x
(
z
+
m
-
-
=
y
x
y
x
0
n
n
)
n
n
(
s
)
y
x

12. (
t
+
m
-
-
=
where
2
n
n
s
)
1
n
(
s
)
1
n
(
s
y
x
2
y
y
2
x
x
2
-
+
-

13. +
-
=
2
n
ˆ
1
0
ˆ
t
2
xy
xy
-
r
-
-
r
=
Chi-square test of association and ANOVA:
å
å
-
=
c
i
j
j
,
i
2

14. j
,
i
j
,
i
2
E
)
E
O
(
k
n
SSW
1
k
SSG
F
-
-
=
where
å
-
=
i
2

15. i
i
)
x
x
(
n
SSG
å
å
-
=
i
j
2
i
j
,
i
)
x
x
(
SSW
Two-variable linear regression model:
å
å
-
å

16. å
å
-
=
b
2
i
2
i
i
i
i
i
2
)
x
(
x
n
y
x
y
x
n
ˆ
or
å
-
å
-
-
=

17. b
2
i
i
i
2
)
x
x
(
)
y
y
)(
x
x
(
ˆ
x
ˆ
y
ˆ
2
1
b
-
=
b
or

18. n
x
ˆ
n
y
ˆ
i
2
i
1
å
b
-
å
=
b
2
n
e
ˆ
2
i
-
å
=
s
å
-
s
=

19. b
2
i
2
)
x
x
(
ˆ
)
ˆ
(
se
t =
)
ˆ
(
se
ˆ
j
j
b
q
-
b
Goodness of fit:
R2 =

20. å
-
å
-
2
i
2
i
)
y
y
(
)
y
y
ˆ
(
2
R =
1
n
)
y
y
(
k
n
e
1
2
i
2
i
-

21. å
-
-
å
-
AIC = ln
å
)
n
/
e
(
2
i
+ 2k/n
F-tests:
F =
k
n
e
1
k
)
y

22. y
ˆ
(
2
i
2
i
-
å
-
å
-
F =
2
2
2
i
1
2
2
2
i
1
2
i
k
n
)
e
(
k

23. k
)
e
(
)
e
(
-
å
-
å
-
å
0
z
0
zTable 1
Area in the upper tail of the standard normal
density function (= ()
z( (
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09

24. 0.0
0.5000
0.4960
0.4920
0.4880
0.4840
0.4801
0.4761
0.4721
0.4681
0.4641
0.1
0.4602
0.4562
0.4522
0.4483
0.4443
0.4404
0.4364
0.4325
0.4286
0.4247
0.2
0.4207
0.4168
0.4129
0.4090
0.4052
0.4013
0.3974
0.3936
0.3897
0.3859
0.3
0.3821
0.3783

25. 0.3745
0.3707
0.3669
0.3632
0.3594
0.3557
0.3520
0.3483
0.4
0.3446
0.3409
0.3372
0.3336
0.3300
0.3264
0.3228
0.3192
0.3156
0.3121
0.5
0.3085
0.3050
0.3015
0.2981
0.2946

26. 0.2912
0.2877
0.2843
0.2810
0.2776
0.6
0.2743
0.2709
0.2676
0.2643
0.2611
0.2578
0.2546
0.2514
0.2483
0.2451
0.7
0.2420
0.2389
0.2358
0.2327
0.2296
0.2266
0.2236
0.2206
0.2177
0.2148
0.8
0.2119
0.2090
0.2061
0.2033
0.2005
0.1977
0.1949
0.1922

27. 0.1894
0.1867
0.9
0.1841
0.1814
0.1788
0.1762
0.1736
0.1711
0.1685
0.1660
0.1635
0.1611
1.0
0.1587
0.1562
0.1539
0.1515
0.1492
0.1469
0.1446
0.1423
0.1401
0.1379
1.1

28. 0.1357
0.1335
0.1314
0.1292
0.1271
0.1251
0.1230
0.1210
0.1190
0.1170
1.2
0.1151
0.1131
0.1112
0.1093
0.1075
0.1056
0.1038
0.1020
0.1003
0.0985
1.3
0.0968
0.0951
0.0934
0.0918
0.0901
0.0885
0.0869
0.0853
0.0838
0.0823
1.4
0.0808
0.0793
0.0778

29. 0.0764
0.0749
0.0735
0.0721
0.0708
0.0694
0.0681
1.5
0.0668
0.0655
0.0643
0.0630
0.0618
0.0606
0.0594
0.0582
0.0571
0.0559
1.6
0.0548
0.0537
0.0526
0.0516
0.0505
0.0495

30. 0.0485
0.0475
0.0465
0.0455
1.7
0.0446
0.0436
0.0427
0.0418
0.0409
0.0401
0.0392
0.0384
0.0375
0.0367
1.8
0.0359
0.0351
0.0344
0.0336
0.0329
0.0322
0.0314
0.0307
0.0301
0.0294
1.9
0.0287
0.0281
0.0274
0.0268
0.0262
0.0256
0.0250
0.0244
0.0239

31. 0.0233
2.0
0.0228
0.0222
0.0217
0.0212
0.0207
0.0202
0.0197
0.0192
0.0188
0.0183
2.1
0.0179
0.0174
0.0170
0.0166
0.0162
0.0158
0.0154
0.0150
0.0146
0.0143
2.2
0.0139

32. 0.0136
0.0132
0.0129
0.0125
0.0122
0.0119
0.0116
0.0113
0.0110
2.3
0.0107
0.0104
0.0102
0.0099
0.0096
0.0094
0.0091
0.0089
0.0087
0.0084
2.4
0.0082
0.0080
0.0078
0.0075
0.0073
0.0071
0.0069
0.0068
0.0066
0.0064

33. 2.5
0.0062
0.0060
0.0059
0.0057
0.0055
0.0054
0.0052
0.0051
0.0049
0.0048
2.6
0.0047
0.0045
0.0044
0.0043
0.0041
0.0040
0.0039
0.0038
0.0037
0.0036
2.7
0.0035
0.0034
0.0033
0.0032
0.0031
0.0030
0.0029

34. 0.0028
0.0027
0.0026
2.8
0.0026
0.0025
0.0024
0.0023
0.0023
0.0022
0.0021
0.0021
0.0020
0.0019
2.9
0.0019
0.0018
0.0018
0.0017
0.0016
0.0016
0.0015
0.0015
0.0014
0.0014
3.0
0.0013
0.0013
0.0013
0.0012
0.0012
0.0011
0.0011
0.0011
0.0010
0.0010

35. Table 2
0
t
0
t
Critical values for the t distribution for various
probability levels (() and degrees of freedom (()
((
((
0.25
0.2
0.15
0.1
0.05
0.025
0.01
0.005

36. 0.0025
1
1.0000
1.3764
1.9626
3.0777
6.3137
12.7062
31.8210
63.6559
127.321
2
0.8165
1.0607
1.3862
1.8856
2.9200
4.3027
6.9645
9.9250
14.0892
3
0.7649
0.9785
1.2498
1.6377
2.3534
3.1824
4.5407
5.8408
7.4532
4

37. 0.7407
0.9410
1.1896
1.5332
2.1318
2.7765
3.7469
4.6041
5.5975
5
0.7267
0.9195
1.1558
1.4759
2.0150
2.5706
3.3649
4.0321
4.7733
6
0.7176
0.9057
1.1342
1.4398
1.9432
2.4469

38. 3.1427
3.7074
4.3168
7
0.7111
0.8960
1.1192
1.4149
1.8946
2.3646
2.9979
3.4995
4.0294
8
0.7064
0.8889
1.1081
1.3968
1.8595
2.3060
2.8965
3.3554
3.8325
9
0.7027
0.8834
1.0997
1.3830
1.8331
2.2622
2.8214
3.2498
3.6896
10
0.6998
0.8791

39. 1.0931
1.3722
1.8125
2.2281
2.7638
3.1693
3.5814
11
0.6974
0.8755
1.0877
1.3634
1.7959
2.2010
2.7181
3.1058
3.4966
12
0.6955
0.8726
1.0832
1.3562
1.7823
2.1788
2.6810
3.0545

40. 3.4284
13
0.6938
0.8702
1.0795
1.3502
1.7709
2.1604
2.6503
3.0123
3.3725
14
0.6924
0.8681
1.0763
1.3450
1.7613
2.1448
2.6245
2.9768
3.3257
15
0.6912
0.8662
1.0735
1.3406
1.7531
2.1315
2.6025
2.9467
3.2860

41. 16
0.6901
0.8647
1.0711
1.3368
1.7459
2.1199
2.5835
2.9208
3.2520
17
0.6892
0.8633
1.0690
1.3334
1.7396
2.1098
2.5669
2.8982
3.2224
18
0.6884
0.8620
1.0672
1.3304
1.7341
2.1009
2.5524
2.8784
3.1966
19

42. 0.6876
0.8610
1.0655
1.3277
1.7291
2.0930
2.5395
2.8609
3.1737
20
0.6870
0.8600
1.0640
1.3253
1.7247
2.0860
2.5280
2.8453
3.1534
21
0.6864
0.8591
1.0627
1.3232
1.7207
2.0796

43. 2.5176
2.8314
3.1352
22
0.6858
0.8583
1.0614
1.3212
1.7171
2.0739
2.5083
2.8188
3.1188
23
0.6853
0.8575
1.0603
1.3195
1.7139
2.0687
2.4999
2.8073
3.1040
24
0.6848
0.8569
1.0593
1.3178
1.7109
2.0639
2.4922
2.7970
3.0905
25
0.6844
0.8562

44. 1.0584
1.3163
1.7081
2.0595
2.4851
2.7874
3.0782
26
0.6840
0.8557
1.0575
1.3150
1.7056
2.0555
2.4786
2.7787
3.0669
27
0.6837
0.8551
1.0567
1.3137
1.7033
2.0518
2.4727
2.7707

45. 3.0565
28
0.6834
0.8546
1.0560
1.3125
1.7011
2.0484
2.4671
2.7633
3.0470
29
0.6830
0.8542
1.0553
1.3114
1.6991
2.0452
2.4620
2.7564
3.0380
30
0.6828
0.8538
1.0547
1.3104
1.6973
2.0423
2.4573
2.7500
3.0298

46. 40
0.6807
0.8507
1.0500
1.3031
1.6839
2.0211
2.4233
2.7045
2.9712
60
0.6786
0.8477
1.0455
1.2958
1.6706
2.0003
2.3901
2.6603
2.9146
120
0.6765
0.8446
1.0409
1.2886
1.6576
1.9799
2.3578
2.6174
2.8599
(

47. 0.6745
0.8416
1.0364
1.2816
1.6449
1.9600
2.3264
2.5759
2.8071
Table 3
0
X
0
XCritical values for the (2 distribution for various
probability levels (() and degrees of freedom (()
Example
For (=10, prob((2>15.987) = 0.1
prob((2>20.483) = 0.025
((
((
0.995
0.99
0.975
0.95

48. 0.9
0.75
0.5
0.25
0.1
0.05
0.025
0.01
0.005
1
0.000
0.000
0.001
0.004
0.016
0.102

49. 0.455
1.323
2.706
3.841
5.024
6.635
7.879
2
0.010
0.020
0.051
0.103
0.211
0.575
1.386
2.773
4.605
5.991
7.378
9.210
10.597
3
0.072
0.115
0.216
0.352
0.584
1.213
2.366
4.108
6.251
7.815
9.348
11.345
12.838
4

50. 0.207
0.297
0.484
0.711
1.064
1.923
3.357
5.385
7.779
9.488
11.143
13.277
14.860
5
0.412
0.554
0.831
1.145
1.610
2.675
4.351
6.626
9.236
11.070
12.832
15.086
16.750

51. 6
0.676
0.872
1.237
1.635
2.204
3.455
5.348
7.841
10.645
12.592
14.449
16.812
18.548
7
0.989
1.239
1.690
2.167
2.833
4.255
6.346
9.037
12.017
14.067
16.013
18.475
20.278
8
1.344
1.647

52. 2.180
2.733
3.490
5.071
7.344
10.219
13.362
15.507
17.535
20.090
21.955
9
1.735
2.088
2.700
3.325
4.168
5.899
8.343
11.389
14.684
16.919
19.023
21.666
23.589
10
2.156
2.558
3.247
3.940
4.865
6.737
9.342
12.549
15.987
18.307

53. 20.483
23.209
25.188
11
2.603
3.053
3.816
4.575
5.578
7.584
10.341
13.701
17.275
19.675
21.920
24.725
26.757
12
3.074
3.571
4.404
5.226

54. 6.304
8.438
11.340
14.845
18.549
21.026
23.337
26.217
28.300
13
3.565
4.107
5.009
5.892
7.041
9.299
12.340
15.984
19.812
22.362
24.736
27.688
29.819
14
4.075
4.660
5.629
6.571
7.790
10.165
13.339
17.117
21.064
23.685
26.119
29.141

55. 31.319
15
4.601
5.229
6.262
7.261
8.547
11.037
14.339
18.245
22.307
24.996
27.488
30.578
32.801
16
5.142
5.812
6.908
7.962
9.312
11.912

56. 15.338
19.369
23.542
26.296
28.845
32.000
34.267
17
5.697
6.408
7.564
8.672
10.085
12.792
16.338
20.489
24.769
27.587
30.191
33.409
35.718
18
6.265
7.015
8.231
9.390
10.865
13.675
17.338
21.605
25.989
28.869
31.526
34.805
37.156
19

57. 6.844
7.633
8.907
10.117
11.651
14.562
18.338
22.718
27.204
30.144
32.852
36.191
38.582
20
7.434
8.260
9.591
10.851
12.443
15.452
19.337
23.828
28.412
31.410
34.170
37.566
39.997

58. 21
8.034
8.897
10.283
11.591
13.240
16.344
20.337
24.935
29.615
32.671
35.479
38.932
41.401
22
8.643
9.542
10.982
12.338
14.041
17.240
21.337
26.039
30.813
33.924
36.781
40.289
42.796
23
9.260
10.196

59. 11.689
13.091
14.848
18.137
22.337
27.141
32.007
35.172
38.076
41.638
44.181
24
9.886
10.856
12.401
13.848
15.659
19.037
23.337
28.241
33.196
36.415
39.364
42.980
45.558
25
10.520
11.524
13.120
14.611
16.473
19.939
24.337
29.339
34.382
37.652

60. 40.646
44.314
46.928
30
13.787
14.953
16.791
18.493
20.599
24.478
29.336
34.800
40.256
43.773
46.979
50.892
53.672
40
20.707
22.164
24.433
26.509

61. 29.051
33.660
39.335
45.616
51.805
55.758
59.342
63.691
66.766
50
27.991
29.707
32.357
34.764
37.689
42.942
49.335
56.334
63.167
67.505
71.420
76.154
79.490
60
35.534
37.485
40.482
43.188
46.459
52.294
59.335
66.981
74.397
79.082
83.298
88.379

62. 91.952
70
43.275
45.442
48.758
51.739
55.329
61.698
69.334
77.577
85.527
90.531
95.021
100.43
104.22
80
51.172
53.540
57.153
60.391
64.278
71.145

63. 79.334
88.130
96.578
101.88
106.63
112.33
116.32
90
59.196
61.754
65.647
69.126
73.291
80.625
89.334
98.650
107.57
113.15
118.14
124.12
128.30
100
67.328
70.065
74.222
77.929
82.358
90.133
99.334
109.14
118.50
124.34
129.56
135.81
140.17

64. Z
-2.576
-2.326
-1.960
-1.645
-1.282
-0.674
0.000
0.674
1.282
1.645
1.960
2.326
2.576
Note: For (>100, use
2
2
)
1
2
z
(
2

65. 1
-
n
+
=
c
, where z = standardized normal deviate shown in the bottom
row of the table.
Table 4a
Critical values for the F distribution, (=0.01, degrees of
freedom = (1, (2
Example
For (1=4, (2=20, prob(F>4.43) = 0.01
(1(
(2(
1
2
3
4
5
6

66. 7
8
9
10
12
15
20
30
50
100
200
500

67. (
1
4052
4999
5404
5624
5764
5859
5928
5981
6022
6056
6107
6157
6209
6260
6302
6334
6350
6360
6366
2
98.5
99.0
99.2
99.3
99.3
99.3
99.4
99.4
99.4
99.4
99.4
99.4
99.4

68. 99.5
99.5
99.5
99.5
99.5
99.5
3
34.1
30.8
29.5
28.7
28.2
27.9
27.7
27.5
27.3
27.2
27.1
26.9
26.7
26.5
26.4
26.2
26.2
26.1
26.1
4
21.2
18.0
16.7
16.0
15.5
15.2
15.0
14.8
14.7

69. 14.5
14.4
14.2
14.0
13.8
13.7
13.6
13.5
13.5
13.5
5
16.3
13.3
12.1
11.4
11.0
10.7
10.5
10.3
10.2
10.1
9.89
9.72
9.55
9.38
9.24
9.13
9.08
9.04
9.02
6
13.7
10.9
9.78
9.15
8.75

70. 8.47
8.26
8.10
7.98
7.87
7.72
7.56
7.40
7.23
7.09
6.99
6.93
6.90
6.88
7
12.2
9.55
8.45
7.85
7.46
7.19
6.99
6.84
6.72
6.62
6.47
6.31
6.16
5.99
5.86
5.75
5.70
5.67
5.65
8
11.3

71. 8.65
7.59
7.01
6.63
6.37
6.18
6.03
5.91
5.81
5.67
5.52
5.36
5.20
5.07
4.96
4.91
4.88
4.86
9
10.6
8.02
6.99
6.42
6.06
5.80
5.61
5.47
5.35
5.26
5.11
4.96
4.81
4.65
4.52
4.41
4.36

72. 4.33
4.31
10
10.0
7.56
6.55
5.99
5.64
5.39
5.20
5.06
4.94
4.85
4.71
4.56
4.41
4.25
4.12
4.01
3.96
3.93
3.91
11
9.65
7.21
6.22
5.67
5.32
5.07
4.89
4.74
4.63
4.54
4.40
4.25
4.10

73. 3.94
3.81
3.71
3.66
3.62
3.60
12
9.33
6.93
5.95
5.41
5.06
4.82
4.64
4.50
4.39
4.30
4.16
4.01
3.86
3.70
3.57
3.47
3.41
3.38
3.36
13
9.07
6.70
5.74
5.21
4.86
4.62
4.44
4.30
4.19

74. 4.10
3.96
3.82
3.66
3.51
3.38
3.27
3.22
3.19
3.17
14
8.86
6.51
5.56
5.04
4.69
4.46
4.28
4.14
4.03
3.94
3.80
3.66
3.51
3.35
3.22
3.11
3.06
3.03
3.00
15
8.68
6.36
5.42
4.89
4.56

75. 4.32
4.14
4.00
3.89
3.80
3.67
3.52
3.37
3.21
3.08
2.98
2.92
2.89
2.87
16
8.53
6.23
5.29
4.77
4.44
4.20
4.03
3.89
3.78
3.69
3.55
3.41
3.26
3.10
2.97
2.86
2.81
2.78
2.75
17
8.40

76. 6.11
5.19
4.67
4.34
4.10
3.93
3.79
3.68
3.59
3.46
3.31
3.16
3.00
2.87
2.76
2.71
2.68
2.65
18
8.29
6.01
5.09
4.58
4.25
4.01
3.84
3.71
3.60
3.51
3.37
3.23
3.08
2.92
2.78
2.68
2.62

77. 2.59
2.57
19
8.18
5.93
5.01
4.50
4.17
3.94
3.77
3.63
3.52
3.43
3.30
3.15
3.00
2.84
2.71
2.60
2.55
2.51
2.49
20
8.10
5.85
4.94
4.43
4.10
3.87
3.70
3.56
3.46
3.37
3.23
3.09
2.94

78. 2.78
2.64
2.54
2.48
2.44
2.42
21
8.02
5.78
4.87
4.37
4.04
3.81
3.64
3.51
3.40
3.31
3.17
3.03
2.88
2.72
2.58
2.48
2.42
2.38
2.36
22
7.95
5.72
4.82
4.31
3.99
3.76
3.59
3.45
3.35

79. 3.26
3.12
2.98
2.83
2.67
2.53
2.42
2.36
2.33
2.31
23
7.88
5.66
4.76
4.26
3.94
3.71
3.54
3.41
3.30
3.21
3.07
2.93
2.78
2.62
2.48
2.37
2.32
2.28
2.26
24
7.82
5.61
4.72
4.22
3.90

80. 3.67
3.50
3.36
3.26
3.17
3.03
2.89
2.74
2.58
2.44
2.33
2.27
2.24
2.21
25
7.77
5.57
4.68
4.18
3.85
3.63
3.46
3.32
3.22
3.13
2.99
2.85
2.70
2.54
2.40
2.29
2.23
2.19
2.17
26
7.72

81. 5.53
4.64
4.14
3.82
3.59
3.42
3.29
3.18
3.09
2.96
2.81
2.66
2.50
2.36
2.25
2.19
2.16
2.13
27
7.68
5.49
4.60
4.11
3.78
3.56
3.39
3.26
3.15
3.06
2.93
2.78
2.63
2.47
2.33
2.22
2.16

82. 2.12
2.10
28
7.64
5.45
4.57
4.07
3.75
3.53
3.36
3.23
3.12
3.03
2.90
2.75
2.60
2.44
2.30
2.19
2.13
2.09
2.06
29
7.60
5.42
4.54
4.04
3.73
3.50
3.33
3.20
3.09
3.00
2.87
2.73
2.57

83. 2.41
2.27
2.16
2.10
2.06
2.03
30
7.56
5.39
4.51
4.02
3.70
3.47
3.30
3.17
3.07
2.98
2.84
2.70
2.55
2.39
2.25
2.13
2.07
2.03
2.01
35
7.42
5.27
4.40
3.91
3.59
3.37
3.20
3.07
2.96

84. 2.88
2.74
2.60
2.44
2.28
2.14
2.02
1.96
1.92
1.96
40
7.31
5.18
4.31
3.83
3.51
3.29
3.12
2.99
2.89
2.80
2.66
2.52
2.37
2.20
2.06
1.94
1.87
1.83
1.80
45
7.23
5.11
4.25
3.77
3.45

85. 3.23
3.07
2.94
2.83
2.74
2.61
2.46
2.31
2.14
2.00
1.88
1.81
1.77
1.78
50
7.17
5.06
4.20
3.72
3.41
3.19
3.02
2.89
2.78
2.70
2.56
2.42
2.27
2.10
1.95
1.82
1.76
1.71
1.68
60
7.08

86. 4.98
4.13
3.65
3.34
3.12
2.95
2.82
2.72
2.63
2.50
2.35
2.20
2.03
1.88
1.75
1.68
1.63
1.60
70
7.01
4.92
4.07
3.60
3.29
3.07
2.91
2.78
2.67
2.59
2.45
2.31
2.15
1.98
1.83
1.70
1.62

87. 1.57
1.54
80
6.96
4.88
4.04
3.56
3.26
3.04
2.87
2.74
2.64
2.55
2.42
2.27
2.12
1.94
1.79
1.65
1.58
1.53
1.49
100
6.90
4.82
3.98
3.51
3.21
2.99
2.82
2.69
2.59
2.50
2.37
2.22
2.07

88. 1.89
1.74
1.60
1.52
1.47
1.43
150
6.81
4.75
3.91
3.45
3.14
2.92
2.76
2.63
2.53
2.44
2.31
2.16
2.00
1.83
1.66
1.52
1.43
1.38
1.33
200
6.76
4.71
3.88
3.41
3.11
2.89
2.73
2.60
2.50

89. 2.41
2.27
2.13
1.97
1.79
1.63
1.48
1.39
1.33
1.28
400
6.70
4.66
3.83
3.37
3.06
2.85
2.68
2.56
2.45
2.37
2.23
2.08
1.92
1.75
1.58
1.42
1.32
1.25
1.19
1000
6.66
4.63
3.80
3.34
3.04

90. 2.82
2.66
2.53
2.43
2.34
2.20
2.06
1.90
1.72
1.54
1.38
1.28
1.19
1.11
(
6.63
4.61
3.78
3.32
3.02
2.80
2.64
2.51
2.41
2.32
2.18
2.04
1.88
1.70
1.52
1.36
1.25
1.15
1.00
Table 4b
Critical values for the F distribution, (=0.025, degrees of

91. freedom = (1, (2
(1(
(2(
1
2
3
4
5
6
7
8
9
10
12

92. 15
20
30
50
100
200
500
(
1
648
799
864
900
922
937
948
957
963
969
977
985

93. 993
1001
1008
1013
1016
1017
1018
2
38.5
39.0
39.2
39.2
39.3
39.3
39.4
39.4
39.4
39.4
39.4
39.4
39.4
39.5
39.5
39.5
39.5
39.5
39.5
3
17.4
16.0
15.4
15.1
14.9
14.7
14.6
14.5

94. 14.5
14.4
14.3
14.3
14.2
14.1
14.0
14.0
13.9
13.9
13.9
4
12.2
10.6
10.0
9.60
9.36
9.20
9.07
8.98
8.90
8.84
8.75
8.66
8.56
8.46
8.38
8.32
8.29
8.27
8.26
5
10.0
8.43
7.76
7.39

95. 7.15
6.98
6.85
6.76
6.68
6.62
6.52
6.43
6.33
6.23
6.14
6.08
6.05
6.03
6.02
6
8.81
7.26
6.60
6.23
5.99
5.82
5.70
5.60
5.52
5.46
5.37
5.27
5.17
5.07
4.98
4.92
4.88
4.86
4.85
7

96. 8.07
6.54
5.89
5.52
5.29
5.12
4.99
4.90
4.82
4.76
4.67
4.57
4.47
4.36
4.28
4.21
4.18
4.16
4.14
8
7.57
6.06
5.42
5.05
4.82
4.65
4.53
4.43
4.36
4.30
4.20
4.10
4.00
3.89
3.81
3.74

97. 3.70
3.68
3.67
9
7.21
5.71
5.08
4.72
4.48
4.32
4.20
4.10
4.03
3.96
3.87
3.77
3.67
3.56
3.47
3.40
3.37
3.35
3.33
10
6.94
5.46
4.83
4.47
4.24
4.07
3.95
3.85
3.78
3.72
3.62
3.52

98. 3.42
3.31
3.22
3.15
3.12
3.09
3.08
11
6.72
5.26
4.63
4.28
4.04
3.88
3.76
3.66
3.59
3.53
3.43
3.33
3.23
3.12
3.03
2.96
2.92
2.90
2.88
12
6.55
5.10
4.47
4.12
3.89
3.73
3.61
3.51

99. 3.44
3.37
3.28
3.18
3.07
2.96
2.87
2.80
2.76
2.74
2.72
13
6.41
4.97
4.35
4.00
3.77
3.60
3.48
3.39
3.31
3.25
3.15
3.05
2.95
2.84
2.74
2.67
2.63
2.61
2.60
14
6.30
4.86
4.24
3.89

100. 3.66
3.50
3.38
3.29
3.21
3.15
3.05
2.95
2.84
2.73
2.64
2.56
2.53
2.50
2.49
15
6.20
4.77
4.15
3.80
3.58
3.41
3.29
3.20
3.12
3.06
2.96
2.86
2.76
2.64
2.55
2.47
2.44
2.41
2.40
16

101. 6.12
4.69
4.08
3.73
3.50
3.34
3.22
3.12
3.05
2.99
2.89
2.79
2.68
2.57
2.47
2.40
2.36
2.33
2.32
17
6.04
4.62
4.01
3.66
3.44
3.28
3.16
3.06
2.98
2.92
2.82
2.72
2.62
2.50
2.41
2.33

102. 2.29
2.26
2.25
18
5.98
4.56
3.95
3.61
3.38
3.22
3.10
3.01
2.93
2.87
2.77
2.67
2.56
2.44
2.35
2.27
2.23
2.20
2.19
19
5.92
4.51
3.90
3.56
3.33
3.17
3.05
2.96
2.88
2.82
2.72
2.62

103. 2.51
2.39
2.30
2.22
2.18
2.15
2.13
20
5.87
4.46
3.86
3.51
3.29
3.13
3.01
2.91
2.84
2.77
2.68
2.57
2.46
2.35
2.25
2.17
2.13
2.10
2.09
21
5.83
4.42
3.82
3.48
3.25
3.09
2.97
2.87

104. 2.80
2.73
2.64
2.53
2.42
2.31
2.21
2.13
2.09
2.06
2.04
22
5.79
4.38
3.78
3.44
3.22
3.05
2.93
2.84
2.76
2.70
2.60
2.50
2.39
2.27
2.17
2.09
2.05
2.02
2.00
23
5.75
4.35
3.75
3.41

105. 3.18
3.02
2.90
2.81
2.73
2.67
2.57
2.47
2.36
2.24
2.14
2.06
2.01
1.99
1.97
24
5.72
4.32
3.72
3.38
3.15
2.99
2.87
2.78
2.70
2.64
2.54
2.44
2.33
2.21
2.11
2.02
1.98
1.95
1.94
25

106. 5.69
4.29
3.69
3.35
3.13
2.97
2.85
2.75
2.68
2.61
2.51
2.41
2.30
2.18
2.08
2.00
1.95
1.92
1.91
26
5.66
4.27
3.67
3.33
3.10
2.94
2.82
2.73
2.65
2.59
2.49
2.39
2.28
2.16
2.05
1.97

107. 1.92
1.90
1.88
27
5.63
4.24
3.65
3.31
3.08
2.92
2.80
2.71
2.63
2.57
2.47
2.36
2.25
2.13
2.03
1.94
1.90
1.87
1.85
28
5.61
4.22
3.63
3.29
3.06
2.90
2.78
2.69
2.61
2.55
2.45
2.34

108. 2.23
2.11
2.01
1.92
1.88
1.85
1.83
29
5.59
4.20
3.61
3.27
3.04
2.88
2.76
2.67
2.59
2.53
2.43
2.32
2.21
2.09
1.99
1.90
1.86
1.83
1.81
30
5.57
4.18
3.59
3.25
3.03
2.87
2.75
2.65

109. 2.57
2.51
2.41
2.31
2.20
2.07
1.97
1.88
1.84
1.81
1.79
35
5.48
4.11
3.52
3.18
2.96
2.80
2.68
2.58
2.50
2.44
2.34
2.23
2.12
2.00
1.89
1.80
1.75
1.72
1.70
40
5.42
4.05
3.46
3.13

110. 2.90
2.74
2.62
2.53
2.45
2.39
2.29
2.18
2.07
1.94
1.83
1.74
1.69
1.66
1.64
45
5.38
4.01
3.42
3.09
2.86
2.70
2.58
2.49
2.41
2.35
2.25
2.14
2.03
1.90
1.79
1.69
1.64
1.61
1.59
50

111. 5.34
3.97
3.39
3.05
2.83
2.67
2.55
2.46
2.38
2.32
2.22
2.11
1.99
1.87
1.75
1.66
1.60
1.57
1.55
60
5.29
3.93
3.34
3.01
2.79
2.63
2.51
2.41
2.33
2.27
2.17
2.06
1.94
1.82
1.70
1.60

112. 1.54
1.51
1.48
70
5.25
3.89
3.31
2.97
2.75
2.59
2.47
2.38
2.30
2.24
2.14
2.03
1.91
1.78
1.66
1.56
1.50
1.46
1.44
80
5.22
3.86
3.28
2.95
2.73
2.57
2.45
2.35
2.28
2.21
2.11
2.00

113. 1.88
1.75
1.63
1.53
1.47
1.43
1.40
100
5.18
3.83
3.25
2.92
2.70
2.54
2.42
2.32
2.24
2.18
2.08
1.97
1.85
1.71
1.59
1.48
1.42
1.38
1.35
150
5.13
3.78
3.20
2.87
2.65
2.49
2.37
2.28

114. 2.20
2.13
2.03
1.92
1.80
1.67
1.54
1.42
1.35
1.31
1.27
200
5.10
3.76
3.18
2.85
2.63
2.47
2.35
2.26
2.18
2.11
2.01
1.90
1.78
1.64
1.51
1.39
1.32
1.27
1.23
400
5.06
3.72
3.15
2.82

115. 2.60
2.44
2.32
2.22
2.15
2.08
1.98
1.87
1.74
1.60
1.47
1.35
1.27
1.21
1.15
1000
5.04
3.70
3.13
2.80
2.58
2.42
2.30
2.20
2.13
2.06
1.96
1.85
1.72
1.58
1.45
1.32
1.23
1.16
1.09
(

116. 5.02
3.69
3.12
2.79
2.57
2.41
2.29
2.19
2.11
2.05
1.94
1.83
1.71
1.57
1.43
1.30
1.21
1.13
1.00
Table 4c
Critical values for the F distribution, (=0.05, degrees of
freedom = (1, (2
(1(
(2(
1
2
3
4

117. 5
6
7
8
9
10
12
15
20
30
50
100

118. 200
500
(
1
161
199
216
225
230
234
237
239
241
242
244
246
248
250
252
253
254
254
254
2
18.5
19.0
19.2
19.2
19.3
19.3
19.4

119. 19.4
19.4
19.4
19.4
19.4
19.4
19.5
19.5
19.5
19.5
19.5
19.5
3
10.1
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
8.79
8.74
8.70
8.66
8.62
8.58
8.55
8.54
8.53
8.53
4
7.71
6.94
6.59

120. 6.39
6.26
6.16
6.09
6.04
6.00
5.96
5.91
5.86
5.80
5.75
5.70
5.66
5.65
5.64
5.63
5
6.61
5.79
5.41
5.19
5.05
4.95
4.88
4.82
4.77
4.74
4.68
4.62
4.56
4.50
4.44
4.41
4.39
4.37
4.37

121. 6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
4.06
4.00
3.94
3.87
3.81
3.75
3.71
3.69
3.68
3.67
7
5.59
4.74
4.35
4.12
3.97
3.87
3.79
3.73
3.68
3.64
3.57
3.51
3.44
3.38
3.32

122. 3.27
3.25
3.24
3.23
8
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
3.35
3.28
3.22
3.15
3.08
3.02
2.97
2.95
2.94
2.93
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
3.23
3.18
3.14
3.07

123. 3.01
2.94
2.86
2.80
2.76
2.73
2.72
2.71
10
4.96
4.10
3.71
3.48
3.33
3.22
3.14
3.07
3.02
2.98
2.91
2.85
2.77
2.70
2.64
2.59
2.56
2.55
2.54
11
4.84
3.98
3.59
3.36
3.20
3.09
3.01

124. 2.95
2.90
2.85
2.79
2.72
2.65
2.57
2.51
2.46
2.43
2.42
2.40
12
4.75
3.89
3.49
3.26
3.11
3.00
2.91
2.85
2.80
2.75
2.69
2.62
2.54
2.47
2.40
2.35
2.32
2.31
2.30
13
4.67
3.81
3.41

125. 3.18
3.03
2.92
2.83
2.77
2.71
2.67
2.60
2.53
2.46
2.38
2.31
2.26
2.23
2.22
2.21
14
4.60
3.74
3.34
3.11
2.96
2.85
2.76
2.70
2.65
2.60
2.53
2.46
2.39
2.31
2.24
2.19
2.16
2.14
2.13

126. 15
4.54
3.68
3.29
3.06
2.90
2.79
2.71
2.64
2.59
2.54
2.48
2.40
2.33
2.25
2.18
2.12
2.10
2.08
2.07
16
4.49
3.63
3.24
3.01
2.85
2.74
2.66
2.59
2.54
2.49
2.42
2.35
2.28
2.19
2.12

127. 2.07
2.04
2.02
2.01
17
4.45
3.59
3.20
2.96
2.81
2.70
2.61
2.55
2.49
2.45
2.38
2.31
2.23
2.15
2.08
2.02
1.99
1.97
1.96
18
4.41
3.55
3.16
2.93
2.77
2.66
2.58
2.51
2.46
2.41
2.34

128. 2.27
2.19
2.11
2.04
1.98
1.95
1.93
1.92
19
4.38
3.52
3.13
2.90
2.74
2.63
2.54
2.48
2.42
2.38
2.31
2.23
2.16
2.07
2.00
1.94
1.91
1.89
1.88
20
4.35
3.49
3.10
2.87
2.71
2.60
2.51

129. 2.45
2.39
2.35
2.28
2.20
2.12
2.04
1.97
1.91
1.88
1.86
1.84
21
4.32
3.47
3.07
2.84
2.68
2.57
2.49
2.42
2.37
2.32
2.25
2.18
2.10
2.01
1.94
1.88
1.84
1.83
1.81
22
4.30
3.44
3.05

130. 2.82
2.66
2.55
2.46
2.40
2.34
2.30
2.23
2.15
2.07
1.98
1.91
1.85
1.82
1.80
1.78
23
4.28
3.42
3.03
2.80
2.64
2.53
2.44
2.37
2.32
2.27
2.20
2.13
2.05
1.96
1.88
1.82
1.79
1.77
1.76

131. 24
4.26
3.40
3.01
2.78
2.62
2.51
2.42
2.36
2.30
2.25
2.18
2.11
2.03
1.94
1.86
1.80
1.77
1.75
1.73
25
4.24
3.39
2.99
2.76
2.60
2.49
2.40
2.34
2.28
2.24
2.16
2.09
2.01
1.92
1.84

132. 1.78
1.75
1.73
1.71
26
4.23
3.37
2.98
2.74
2.59
2.47
2.39
2.32
2.27
2.22
2.15
2.07
1.99
1.90
1.82
1.76
1.73
1.71
1.69
27
4.21
3.35
2.96
2.73
2.57
2.46
2.37
2.31
2.25
2.20
2.13

133. 2.06
1.97
1.88
1.81
1.74
1.71
1.69
1.67
28
4.20
3.34
2.95
2.71
2.56
2.45
2.36
2.29
2.24
2.19
2.12
2.04
1.96
1.87
1.79
1.73
1.69
1.67
1.65
29
4.18
3.33
2.93
2.70
2.55
2.43
2.35

134. 2.28
2.22
2.18
2.10
2.03
1.94
1.85
1.77
1.71
1.67
1.65
1.64
30
4.17
3.32
2.92
2.69
2.53
2.42
2.33
2.27
2.21
2.16
2.09
2.01
1.93
1.84
1.76
1.70
1.66
1.64
1.62
35
4.12
3.27
2.87

135. 2.64
2.49
2.37
2.29
2.22
2.16
2.11
2.04
1.96
1.88
1.79
1.70
1.63
1.60
1.57
1.56
40
4.08
3.23
2.84
2.61
2.45
2.34
2.25
2.18
2.12
2.08
2.00
1.92
1.84
1.74
1.66
1.59
1.55
1.53
1.51

136. 45
4.06
3.20
2.81
2.58
2.42
2.31
2.22
2.15
2.10
2.05
1.97
1.89
1.81
1.71
1.63
1.55
1.51
1.49
1.47
50
4.03
3.18
2.79
2.56
2.40
2.29
2.20
2.13
2.07
2.03
1.95
1.87
1.78
1.69
1.60

137. 1.52
1.48
1.46
1.44
60
4.00
3.15
2.76
2.53
2.37
2.25
2.17
2.10
2.04
1.99
1.92
1.84
1.75
1.65
1.56
1.48
1.44
1.41
1.39
70
3.98
3.13
2.74
2.50
2.35
2.23
2.14
2.07
2.02
1.97
1.89

138. 1.81
1.72
1.62
1.53
1.45
1.40
1.37
1.35
80
3.96
3.11
2.72
2.49
2.33
2.21
2.13
2.06
2.00
1.95
1.88
1.79
1.70
1.60
1.51
1.43
1.38
1.35
1.32
100
3.94
3.09
2.70
2.46
2.31
2.19
2.10

139. 2.03
1.97
1.93
1.85
1.77
1.68
1.57
1.48
1.39
1.34
1.31
1.28
150
3.90
3.06
2.66
2.43
2.27
2.16
2.07
2.00
1.94
1.89
1.82
1.73
1.64
1.54
1.44
1.34
1.29
1.25
1.22
200
3.89
3.04
2.65

140. 2.42
2.26
2.14
2.06
1.98
1.93
1.88
1.80
1.72
1.62
1.52
1.41
1.32
1.26
1.22
1.19
400
3.86
3.02
2.63
2.39
2.24
2.12
2.03
1.96
1.90
1.85
1.78
1.69
1.60
1.49
1.38
1.28
1.22
1.17
1.13

141. 1000
3.85
3.00
2.61
2.38
2.22
2.11
2.02
1.95
1.89
1.84
1.76
1.68
1.58
1.47
1.36
1.26
1.19
1.13
1.08
(
3.84
3.00
2.60
2.37
2.21
2.10
2.01
1.94
1.88
1.83
1.75
1.67
1.57
1.46
1.35

142. 1.24
1.17
1.11
1.00
Table 4d
Critical values for the F distribution, (=0.1, degrees of freedom
= (1, (2
(1(
(2(
1
2
3
4
5
6
7
8
9

143. 10
12
15
20
30
50
100
200
500
(
1
39.9
49.5
53.6
55.8
57.2
58.2

144. 58.9
59.4
59.9
60.2
60.7
61.2
61.7
62.3
62.7
63.0
63.2
63.3
63.3
2
8.53
9.00
9.16
9.24
9.29
9.33
9.35
9.37
9.38
9.39
9.41
9.42
9.44
9.46
9.47
9.48
9.49
9.49
9.49
3
5.54
5.46

145. 5.39
5.34
5.31
5.28
5.27
5.25
5.24
5.23
5.22
5.20
5.18
5.17
5.15
5.14
5.14
5.14
5.13
4
4.54
4.32
4.19
4.11
4.05
4.01
3.98
3.95
3.94
3.92
3.90
3.87
3.84
3.82
3.80
3.78
3.77
3.76

146. 3.76
5
4.06
3.78
3.62
3.52
3.45
3.40
3.37
3.34
3.32
3.30
3.27
3.24
3.21
3.17
3.15
3.13
3.12
3.11
3.11
6
3.78
3.46
3.29
3.18
3.11
3.05
3.01
2.98
2.96
2.94
2.90
2.87
2.84
2.80

147. 2.77
2.75
2.73
2.73
2.72
7
3.59
3.26
3.07
2.96
2.88
2.83
2.78
2.75
2.72
2.70
2.67
2.63
2.59
2.56
2.52
2.50
2.48
2.48
2.47
8
3.46
3.11
2.92
2.81
2.73
2.67
2.62
2.59
2.56
2.54

148. 2.50
2.46
2.42
2.38
2.35
2.32
2.31
2.30
2.29
9
3.36
3.01
2.81
2.69
2.61
2.55
2.51
2.47
2.44
2.42
2.38
2.34
2.30
2.25
2.22
2.19
2.17
2.17
2.16
10
3.29
2.92
2.73
2.61
2.52
2.46

149. 2.41
2.38
2.35
2.32
2.28
2.24
2.20
2.16
2.12
2.09
2.07
2.06
2.06
11
3.23
2.86
2.66
2.54
2.45
2.39
2.34
2.30
2.27
2.25
2.21
2.17
2.12
2.08
2.04
2.01
1.99
1.98
1.97
12
3.18
2.81

150. 2.61
2.48
2.39
2.33
2.28
2.24
2.21
2.19
2.15
2.10
2.06
2.01
1.97
1.94
1.92
1.91
1.90
13
3.14
2.76
2.56
2.43
2.35
2.28
2.23
2.20
2.16
2.14
2.10
2.05
2.01
1.96
1.92
1.88
1.86
1.85

151. 1.85
14
3.10
2.73
2.52
2.39
2.31
2.24
2.19
2.15
2.12
2.10
2.05
2.01
1.96
1.91
1.87
1.83
1.82
1.80
1.80
15
3.07
2.70
2.49
2.36
2.27
2.21
2.16
2.12
2.09
2.06
2.02
1.97
1.92
1.87

152. 1.83
1.79
1.77
1.76
1.76
16
3.05
2.67
2.46
2.33
2.24
2.18
2.13
2.09
2.06
2.03
1.99
1.94
1.89
1.84
1.79
1.76
1.74
1.73
1.72
17
3.03
2.64
2.44
2.31
2.22
2.15
2.10
2.06
2.03
2.00

153. 1.96
1.91
1.86
1.81
1.76
1.73
1.71
1.69
1.69
18
3.01
2.62
2.42
2.29
2.20
2.13
2.08
2.04
2.00
1.98
1.93
1.89
1.84
1.78
1.74
1.70
1.68
1.67
1.66
19
2.99
2.61
2.40
2.27
2.18
2.11

154. 2.06
2.02
1.98
1.96
1.91
1.86
1.81
1.76
1.71
1.67
1.65
1.64
1.63
20
2.97
2.59
2.38
2.25
2.16
2.09
2.04
2.00
1.96
1.94
1.89
1.84
1.79
1.74
1.69
1.65
1.63
1.62
1.61
21
2.96
2.57

155. 2.36
2.23
2.14
2.08
2.02
1.98
1.95
1.92
1.87
1.83
1.78
1.72
1.67
1.63
1.61
1.60
1.59
22
2.95
2.56
2.35
2.22
2.13
2.06
2.01
1.97
1.93
1.90
1.86
1.81
1.76
1.70
1.65
1.61
1.59
1.58

156. 1.57
23
2.94
2.55
2.34
2.21
2.11
2.05
1.99
1.95
1.92
1.89
1.84
1.80
1.74
1.69
1.64
1.59
1.57
1.56
1.55
24
2.93
2.54
2.33
2.19
2.10
2.04
1.98
1.94
1.91
1.88
1.83
1.78
1.73
1.67

157. 1.62
1.58
1.56
1.54
1.53
25
2.92
2.53
2.32
2.18
2.09
2.02
1.97
1.93
1.89
1.87
1.82
1.77
1.72
1.66
1.61
1.56
1.54
1.53
1.52
26
2.91
2.52
2.31
2.17
2.08
2.01
1.96
1.92
1.88
1.86

158. 1.81
1.76
1.71
1.65
1.59
1.55
1.53
1.51
1.50
27
2.90
2.51
2.30
2.17
2.07
2.00
1.95
1.91
1.87
1.85
1.80
1.75
1.70
1.64
1.58
1.54
1.52
1.50
1.49
28
2.89
2.50
2.29
2.16
2.06
2.00

159. 1.94
1.90
1.87
1.84
1.79
1.74
1.69
1.63
1.57
1.53
1.50
1.49
1.48
29
2.89
2.50
2.28
2.15
2.06
1.99
1.93
1.89
1.86
1.83
1.78
1.73
1.68
1.62
1.56
1.52
1.49
1.48
1.47
30
2.88
2.49

160. 2.28
2.14
2.05
1.98
1.93
1.88
1.85
1.82
1.77
1.72
1.67
1.61
1.55
1.51
1.48
1.47
1.46
35
2.85
2.46
2.25
2.11
2.02
1.95
1.90
1.85
1.82
1.79
1.74
1.69
1.63
1.57
1.51
1.47
1.44
1.42

161. 1.41
40
2.84
2.44
2.23
2.09
2.00
1.93
1.87
1.83
1.79
1.76
1.71
1.66
1.61
1.54
1.48
1.43
1.41
1.39
1.38
45
2.82
2.42
2.21
2.07
1.98
1.91
1.85
1.81
1.77
1.74
1.70
1.64
1.58
1.52

162. 1.46
1.41
1.38
1.36
1.35
50
2.81
2.41
2.20
2.06
1.97
1.90
1.84
1.80
1.76
1.73
1.68
1.63
1.57
1.50
1.44
1.39
1.36
1.34
1.33
60
2.79
2.39
2.18
2.04
1.95
1.87
1.82
1.77
1.74
1.71

163. 1.66
1.60
1.54
1.48
1.41
1.36
1.33
1.31
1.29
70
2.78
2.38
2.16
2.03
1.93
1.86
1.80
1.76
1.72
1.69
1.64
1.59
1.53
1.46
1.39
1.34
1.30
1.28
1.27
80
2.77
2.37
2.15
2.02
1.92
1.85

164. 1.79
1.75
1.71
1.68
1.63
1.57
1.51
1.44
1.38
1.32
1.28
1.26
1.24
100
2.76
2.36
2.14
2.00
1.91
1.83
1.78
1.73
1.69
1.66
1.61
1.56
1.49
1.42
1.35
1.29
1.26
1.23
1.21
150
2.74
2.34

165. 2.12
1.98
1.89
1.81
1.76
1.71
1.67
1.64
1.59
1.53
1.47
1.40
1.33
1.26
1.22
1.19
1.17
200
2.73
2.33
2.11
1.97
1.88
1.80
1.75
1.70
1.66
1.63
1.58
1.52
1.46
1.38
1.31
1.24
1.20
1.17

166. 1.14
400
2.72
2.32
2.10
1.96
1.86
1.79
1.73
1.69
1.65
1.61
1.56
1.50
1.44
1.36
1.29
1.21
1.17
1.13
1.10
1000
2.71
2.31
2.09
1.95
1.85
1.78
1.72
1.68
1.64
1.61
1.55
1.49
1.43
1.35

167. 1.27
1.20
1.15
1.10
1.06
(
2.71
2.30
2.08
1.94
1.85
1.77
1.72
1.67
1.63
1.60
1.55
1.49
1.42
1.34
1.26
1.19
1.13
1.08
1.00
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168. _1351553830.unknown
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